Method for decoding linear space-time codes in a multiple-antenna wireless transmission system and decoder therefor

ABSTRACT

An iterative method and a decoder for decoding space-time codes in a communication system with multiple transmission and reception antennae, strikes a compromise between techniques based on interference cancellation algorithms such as BLAST, which show faulty performance concerning error rate based on signal-to-noise ratio and techniques based on maximum likelihood algorithms which are optimal in terms of performance, but highly complex in implantation such as the sphere decoder. Therefor the method includes using a first matrix product between the received signal (Y) and a shaping matrix (B l ), and a second matrix product between a subtraction matrix (D l ) and the vector of the estimated symbols (S 1−l ) during the preceding iteration. The estimated symbols during the current iteration are generated by a subtractor ( 9 ) receiving the results (r l, z l ) of the two matrix products. The role of the matrix D l  is to subtract from the current information symbol S l  the interference caused by the other information symbols.

The present invention relates to a method for decoding linear space-timecodes in a multiple-antenna wireless transmission system. It alsorelates to a decoder implementing this method.

The invention is found to be particularly useful in the field of radiotransmission or broadcasting of digital data, or sampled analog data, inparticular in the case of transmission with mobiles or more generally,in the case of a local or non-local wireless network. More precisely,the invention can be used in particular when high-throughput wirelesstransmissions are to be made. A first category of use relates tocellular communication systems with mobiles such as the UMTS forexample. A second category of use relates to local wireless networks. Athird category of use is that of future ad hoc networks.

Existing and future wireless communication systems require a highquality of transmission for constantly increasing throughputs. In fact,these systems have as an objective the establishing of servicesincluding high quality data and video transmission channels.

There are numerous constraints linked with multi-path propagation. Thismultiple propagation is due to the fact that a radio signal reaches anantenna by several paths via reflections on the ionosphere and onterrestrial objects such as mountains and buildings for example. Theeffects of this multiple propagation are constructive and destructiveinterferences as well as phase shifts of the signals transmitted.

In order to develop a reliable and robust communication system, space,time and frequency diversity techniques are used. Space diversityconsists in particular of an arrangement of several transmit and/orreceive antennae. When time diversity is added, a space-time diversityis created, requiring space-time coding on transmission, as well asspace-time decoding on reception. It is known that space-time codes makeit possible to increase the throughputs of information transmitted foran equal quality of service.

High-efficiency linear space-time codes have already been decoded bydecoding algorithms which can be classified in two families:

-   -   interference cancellation algorithms such as BLAST (“Bell        Laboratories Layered Space-Time”) which have poor performances        in terms of error rates as a function of the signal-to-noise        ratio.    -   maximum likelihood algorithms which are optimal in terms of        performance, but with a high installation complexity such as the        sphere decoder.

The document U.S. Pat. No. 6,178,196 (SESHADRI et al.) is known, whichdescribes a multiple antenna system combining interference cancellationdecoding with maximum likelihood decoding. The system described has thepurpose of isolating the signals originating from a given station,assuming that the symbols of the signals transmitted by another stationare correctly determined during a preliminary estimation.

An optimal decoder for high-yield linear space-time codes has been foundby Damen, Chkeif and Belfiore (O. Damen, A. Chkeif and J.-C. Belfiore,“Lattice Code Decoder for Space-Time Codes,” IEEE CommunicationsLetters, May 2000). Its performances exceed those possible with the“BLAST” decoder (G. D. Golden, G. J. Foschini, R. A. Valenzuela, P. W.Wolniasky, “Detection Algorithm and Initial Laboratory Results using theV-BLAST Space-Time Communication Architecture,” IEEE ElectronicsLetters, Jan. 7, 1999). However, it suffers from three problems closelylinked to its implementation:

-   1. It is of a fairly high complexity, which makes its high    throughput implementation very problematical.-   2. Its complexity strongly depends on the radius of the sphere    chosen. The code word decoded must in fact be found in this sphere    if the decoding is not to fail, and moreover, there must not be many    other code words to be found in this same sphere, as otherwise the    decoding complexity can further increase very considerably.-   3. Finally, the decoding complexity depends very strongly on the    signal-to-noise ratio and also the right choice of sphere. The    sphere choice algorithms are themselves fairly complex. It is    therefore seen to be necessary to find another decoding algorithm    which does not suffer from this kind of problems.

The present invention has the purpose of developing a new linearspace-time decoder realizing a compromise between the interferencecancellation technique and the maximum likelihood technique. Theinvention aims at performances very close to the maximum likelihoodtechnique with simplified implementation compared with that of theinterference cancellation algorithms.

The abovementioned objectives are achieved with an iterative method fordecoding a set of N sampled signals in a space-time communication systemwith M transmit antennae and N receive antennae The N signals areprocessed by intervals of time T corresponding to the time length of thelinear space-time code associated with the transmission signals. In eachtime interval T, the sampled signals received are represented in theform of a signal matrix Y.Y=(y _(ij)) i=1, . . . , Nj=1, . . . , Tcan also be expressed in the form Y=H X+W  (1)in which X is the space-time code word transmitted and is represented bya rectangular matrix with M lines and T columns, H is the channel matrixand is represented by a rectangular matrix with N lines and M columns,and finally W is noise, represented by a rectangular matrix with N linesand T columns.

It is therefore seen that the line changes correspond to the antennachanges whereas the column changes correspond to changes in the samplingtimes. In this model, the coeffecients of the matrix X depend linearlyon the information symbols to be transmitted, i.e. the coefficients ofthe matrix transmitted, x_(ij) with i ranging from 1 to M and j rangingfrom 1 to T are written in the form

$x_{ij} = {\sum\limits_{p = 1}^{M}\;{\sum\limits_{q = 1}^{T}\;{g_{ijpq}S_{pq}}}}$with s_(pq) being the information symbols and g_(ijpq) beingcoefficients which depend on the code chosen. Thus, any linearspace-time code, i.e. such that the words transmitted X have theircoefficients x_(ij), which can be expressed in the preceding form, canbe decoded by the method according to the invention.

A description will now be given of a vectorized model on which themethod according to the invention can be used. Instead of working withmatrices, it is possible to vectorize the expression of the signalreceived in equation (1) and writeY=vec (Y)=H X+W  (2)With x=vec (X)=G S, G has the dimension (MT,MT)

${{And}\mspace{14mu} H} = \begin{bmatrix}H & \; & \; & \; & 0 \\\; & . & \; & \; & \; \\\; & \; & . & \; & \; \\\; & \; & \; & . & \; \\0 & \; & \; & \; & H\end{bmatrix}$

H is a matrix (NT,MT) having on the diagonal T times the matrix H, theother coefficients being zero.

Equation (2) is then equivalent to equation (1) and constitutes itsvectorized version. It is on this version that the decoder of theinvention will be used. It is now sufficient to define the extendedchannel matrixC=H Gwhich will be used hereafter. The vectorized version of the receivedsignal can therefore be rewrittenY=C S+Wwhere Y is a column vector with NT components, C is a matrix NT×MT, S isthe symbols column vector with MT components and W is the noise columnvector with NT components.

The iterative decoding method according to the present invention makesit possible to obtain an estimation of the symbols of the signalstransmitted. This method is used in particular for N greater than orequal to M. According to the invention, it comprises the followingsteps:

-   -   Pre-processing of the vector Y in order to maximize the signal        to noise+interference ratio in order to obtain a signal {tilde        over (r)}^(l).    -   Subtraction from the signal {tilde over (r)}^(l) of a signal        {circumflex over (z)}^(l) by means of a subtractor, the signal        {circumflex over (z)}^(l) being obtained by reconstruction        post-processing of the interference between symbols from the        symbols estimated during the preceding iteration;    -   Detection of the signal generated by the subtractor in order to        obtain, for the iteration in progress, an estimation of the        symbols of the signals transmitted.

The pre-processing step can be carried out by operating a matrixmultiplication between the signal vector Y and a matrix B, the matrix Bbeing updated at each iteration.

The post-processing step can also be carried out by operating a matrixmultiplication between the vector of the symbols estimated during thepreceding iteration and a matrix D, the matrix D being updated at eachiteration.

According to the invention, for each iteration, a standardizedcorrelation coefficient ρ is calculated, the updating of a matrix beingachieved by determining new coefficients of the matrix as a function ofthe correlation coefficient obtained for the preceding iteration.

According to a preferred embodiment of the invention, the N signals areprocessed by time intervals T corresponding to the time length of thelinear space-time code associated with the transmission signals, and thepre-processing step involves the matrix B in order to maximize thesignal to noise+interference ratio, the transfer function of which is:

$B^{l} = {{{{Diag}\left( \frac{1}{{\rho_{l - 1}^{2}A_{i}^{l}} + \frac{N_{0}}{E_{s}}} \right)}1} \leq i \leq {{{MT}.C^{H}}{V^{l}}^{\;}}}$${{{with}\mspace{14mu} V^{l}} = \left\lbrack {{\frac{1 - \rho_{l - 1}^{2}}{\frac{N_{0}}{E_{s}}} \cdot C \cdot C^{H}} + {Id}_{N}} \right\rbrack^{- 1}};{A^{l} = {{diag}\left( {C^{H} \cdot V^{l} \cdot C} \right)}};$l: iteration index; ρ: standardized correlation coefficient between thereal symbols and the estimated symbols; N₀: noise variance; Es: meanenergy of a symbol; C: extended channel matrix.

Similarly, the post-processing step can involve a matrix D for thereconstruction of the interference between symbols, the transferfunction of which is:

$D^{l} = {{{B^{l} \cdot C \cdot \rho_{l - 1}} - {{{Diag}\left( \frac{1}{{\rho_{l - 1}^{2}A_{i}^{l}} + \frac{N_{0}}{E_{s}}} \right)}1}} \leq i \leq {MT}}$

Before the first iteration, we have no information on the symbols. Thematrix B has the role of maximizing the signal/(noise+interference)ratio. The vector z is void. A representation of the vector of thesymbols S can be such that the k^(th) symbol is:S _(k)(received)=S _(k)(transmitted)+Σa _(i) S _(i)(transmitted)+noise

At the second iteration, the matrix B still maximizes the SINR ratio.The matrix D will mimic the interference between symbols, i.e.Σa_(i)S_(i)(transmitted) during the preceding iteration at the level ofthe signal r leaving the matrix B. The subtractor makes it possible tosubtract this interference.

At the last iteration, it is assumed that the symbols are correctlyestimated, i.e. that D makes it possible to reconstruct all theinterference, such that it is estimated that:S _(k)(received)=S _(k)(transmitted)+noise

The invention is a decoder which can be adapted to linear space-timecodes, whatever they are, i.e. it makes it possible to decode any codesuch that the sequences transmitted are written as a linear combinationof the information symbols.

It can be noted that the matrices B and D depend on the correlationcoefficient which is different for each iteration. According to anadvantageous characteristic of the invention, in order to determine thecorrelation coefficient ρ^(l), at each iteration:

-   -   the signal to interference ratio SINR is calculated at the        threshold detector's input using the following formula:

${SINR}^{l} = {\left\lbrack {\frac{1}{\xi^{l}{\mathbb{e}}^{\xi^{l}}{E_{1}\left( \xi^{l} \right)}} - 1} \right\rbrack\frac{1}{1 - \rho_{l - 1}^{2}}}$

-   -    with the integral exponential

${{E_{1}(s)} = {{\int_{s}^{+ \infty}{\frac{{\mathbb{e}}^{- t}}{t}\ {\mathbb{d}t}\mspace{14mu}{and}\mspace{14mu}\xi^{l}}} = \frac{ϛ}{1 - \rho_{l - 1}^{2}}}};{ϛ = \frac{N_{0}}{{NE}_{s}}}$

-   -   the symbol error probability Pr, for example at the threshold        detector's input, is calculated from the signal to interference        ratio SINR^(l); and

the correlation coefficient ρ^(l) is then calculated from the symbolerror probability Pr. In order to do this, it is possible to use astandard formula producing the correlation coefficient as a function ofthe symbol error probability, this formula depending on the modulationused in the transmission.

This results in the most precise possible approximation to thecorrelation coefficient ρ^(l).

In subsequent experiments, four iterations sufficed to obtain very goodresults. But it is also possible to define a minimum value (thresholdvalue) of the correlation coefficient for which the iterations areinterrupted. This coefficient is essentially a function of H, which canbe estimated in standard manner, and of the variance N₀. Consequently,all the values of the correlation coefficient ρ, as well as the valuesof the matrices B and D (for all of the iterations) can be calculatedbefore the first iteration. They can therefore be stored before thefirst iteration in a memory in order to then be brought out for eachiteration.

Preferably, it is assumed that ρ⁰=0.

Moreover, in order to calculate the symbol error probability Pr, it canbe assumed that the total noise is Gaussian and that it is possible touse the formula corresponding to the constellation of a linearmodulation, for example

$Q\left( \sqrt{\frac{{{}_{}^{}{}_{}^{}}^{\;}}{N_{0}}} \right)$for the BPSK (“Binary Phase Shift Keying”) system or to use tablesindicating the error probability as a function of the signal to noiseratio. In fact, depending on the complexity of the symbol errorprobability it can be useful to directly tabulate the formula.

Advantageously, in order to calculate the correlation coefficient ρ^(l)from the symbol error probability Pr, it can be assumed that when thereis an error, the threshold detector detects one of the closestneighbours to the symbol transmitted.

By way of example, at the final iteration, it is possible to introducethe signal leaving the subtractor into a soft-entry decoder.

According to a preferred method of implementation of the invention, theinformation symbols can be elements of a constellation originating froma quadrature amplitude modulation, or QAM.

According to another feature of the invention, a space-time decoder isproposed for decoding a signal vector Y obtained from N sampled signalsin a space-time communication system with M transmit antennae and Nreceive antennae, with N greater than or equal to M, with a view toobtaining an estimation of the symbols of the signals transmitted.According to the invention, this decoder comprises:

-   -   a pre-processing module of the vector Y for maximizing the        signal to noise+interference ratio in order to obtain a signal        {tilde over (r)}^(l),    -   a subtractor for subtracting a signal {circumflex over (x)}^(l)        from the signal {tilde over (r)}^(l),    -   a post-processing module for the reconstruction of the        interference between symbols from the symbols estimated during        the preceding iteration in order to generate the signal        {circumflex over (z)}^(l),    -   a threshold detector for detecting the signal generated by the        subtractor in order to obtain, for the iteration in progress, an        estimation of the symbols of the signals transmitted.

These pre-processing and post-processing modules can be matrices, B andD, according to the formulae indicated previously.

Other advantages and characteristics of the invention will becomeapparent on examining the detailed description of an implementationembodiment which is in no way limitative, and the attached drawings inwhich:

FIG. 1 is a diagram illustrating some elements of a transmission systemwithin a transmitter and a receiver, the space-time decoder according tothe invention being integrated into the receiver;

FIG. 2 is a general diagram illustrating the architecture of thespace-time decoder according to the invention; and

FIG. 3 is a general block diagram according to the invention.

FIG. 1 represents a transmitter 1 provided with a plurality of antennae7. The transmitter 1 comprises in particular, upstream of the antennae,an error correcting encoder 3 followed by a linear space-time encoder 4.According to an advantageous characteristic of the invention, thedecoder according to the invention is capable of being applied to anylinear space-time code, i.e. codes such as the sequences transmitted arewritten as a linear combination of the information symbols.

The signals transmitted by the antennae 7 are picked up by a pluralityof antennae 8 within a receiver 2. The signals received undergoprocessing within a space-time decoder 5 according to the invention inorder to estimate the information symbols of the signals transmitted.The space-time decoder 5 has a soft output to which a soft-input decoderis connected, for decoding error correcting codes such as convolutionalcodes, turbo-codes, Reed-Solomon codes etc.; the decoding being able tobe carried out by a Viterbi algorithm, a MAP (maximum a posteriori)algorithm or iterated LOG-MAP etc.

FIG. 2 illustrates a general diagram of the architecture of thespace-time decoder according to the invention. This decoder implementsan iterative method making it possible to determine the informationsymbols S following a firm decision generated by a threshold detector10. However, the space-time decoder according to the invention alsogenerates information symbols following a soft decision capable of beinginjected into the soft input decoder 6, the injected signal being thesignal obtained during the last iteration. The architecture of thedecoder according to the invention chiefly involves two modules B and Dinjecting their output signals into a subtractor 9. The subtractor 9generates an information symbol vector following a soft decision, thesesymbols being then detected by the threshold detector 10 in order toobtain symbols estimated by firm decision.

The two modules B and D represent matrix products of their input signalsby the matrices B^(l) and D^(l), the index l expressing the iteration inprogress. The module B receives at its input the signal Y from theantennae 8. The product of the matrix BL and Y is a signal {tilde over(r)}^(l) from which is subtracted the signal {circumflex over (z)}^(l)from the matrix product of the matrix D^(l) and the signal s^(l−1). Thematrices B^(l) and D^(l) are such that: by taking up the notations inFIG. 2, we arrive at:{tilde over (r)} ^(l) =B ^(l) ·Ys ^(l) ={tilde over (r)} ^(l) −{circumflex over (z)} ^(l){circumflex over (z)} ^(l) =D ^(l) ·ŝ ^(l−1)

Noting that in the detection of the symbol s_(i) of the vector s, thei^(th) component of {circumflex over (z)}^(l) must not be subtractedfrom {tilde over (r)}^(l), the following constraint is imposed on D^(l):D_(ii) ^(l)=0, ∀1≦i≦ni.e. a zero diagonal in order not to subtract the useful signal.

The detector generates the firm decision ŝ^(l) from {tilde over (s)}^(l)which is expressed in the iteration l by:ŝ ^(l) =B ^(l) ·Y−D ^(l) ·ŝ ^(l−1) =B ^(l)·(H·s+w)−D ^(l) ·ŝ ^(l−1)

The first step to be implemented in the iterative decoder consists ofdetermining the matrices B^(l) and D^(l) such that the mean quadraticerror at the threshold detector input is as small as possible. It isdefined at iteration 1 by the quantity:MSE ^(l)(B ^(l) , D ^(l))=∥{tilde over (s)} ^(l) −s∥ ²Minimizing the following expression means that B^(l) and D^(l) verify

$\frac{\partial{{MSE}^{l}\left( {B^{l},D^{l}} \right)}}{\partial B^{l}} = {\frac{\partial{{MSE}^{l}\left( {B^{l},D^{l}} \right)}}{\partial D^{l}} = 0}$

The solving of these equations makes it possible to obtain, at iterationl as a function of the iteration l−1, the following matrices B^(l) andD^(l):

$B^{l} = {{{{Diag}\left( \frac{1}{{\rho_{l - 1}^{2}A_{i}^{l}} + \frac{N_{0}}{E_{s}}} \right)}1} \leq i \leq {{{MT}.C^{H}}{V^{l}}^{\;}}}$$D^{l} = {{{{B^{l}.C} \cdot \rho_{l - 1}} - {{{Diag}\left( \frac{1}{{\rho_{l - 1}^{2}A_{i}^{l}} + \frac{N_{0}}{E_{s}}} \right)}1}} \leq i \leq {MT}}$With:

$V^{l} = \left\lbrack {{\frac{1 - \rho_{l - 1}^{2}}{\frac{N_{0}}{E_{s}}} \cdot C \cdot C^{H}} + {Id}_{N}} \right\rbrack^{- 1}$andA ^(l=)diag(C ^(H) ·V ^(l) ·C);where E_(s) is the mean energy of the QAM constellation and N₀ is thenoise variance.

The form of the matrix D^(l) is intuitively satisfactory. In fact, ifŝ^(l−1)=s such that ρ^(l−1)=1, then the D^(l) output reproduces theinter-symbol component for each symbol s_(i), ∀1≦i≦M.

In a more general manner, ρ^(l−1)=1 indicates the confidence there is inthe quality of the estimated ŝ^(l−1). If ŝ^(l−1) is not reliable thenρ^(l−1)=1 will be low and consequently a lower weighting will be appliedto the estimator of the inter-symbol interference subtracted from {tildeover (r)}^(l). On the other hand, if ŝ^(l−1) is an excellent estimate ofs, then ρ_(s) ^(l−1)→1 and almost all the inter-symbol interference issubtracted from {tilde over (r)}^(l). It should also be noted that atthe first passage l=1, ρ_(s) ^(l−1)=ρ_(s) ⁰=0 and as there is noestimated ŝ^(l−1)=ŝ⁰ still available, B^(l) is the adapted filter.

In these equations, ρ^(l) designates the value, at iteration l, of thecorrelation between the symbols detected at iteration l, Ŝ_(k) ^(l) andthe symbols actually transmitted. This correlation is therefore

$\rho^{l} = \frac{E\left( {S_{k}{\hat{s}}_{k}^{l}} \right)}{E_{s}}$where E_(s) is the mean energy of a symbol

It can be noted that the matrices B^(l) and D^(l) have very differentroles:

-   -   The matrix B^(l) is a signal-formation matrix. At iteration        zero, it is noted that B^(l) is the linear decoder which        minimizes the mean square error. When the correlation becomes        great (tends towards 1), the role of the matrix B^(l) becomes        marginal.    -   The role of the matrix D^(l) is to subtract from the current        information symbol the interference due to the other information        symbols. Its role is marginal at iteration zero, but as        confidence in the detected symbols ŝ^(l) grows, its role becomes        determinant.

A means of estimating the correlation coefficient will now be described.

Calculation of the correlation

$\rho^{l} = \frac{E\left( {S_{k}{\hat{s}}_{k}^{l}} \right)}{E_{s}}$requires calculation of the signal to interference ratio at iteration l,SINR^(l). This signal to interference noise ratio is first calculated asa function of the correlation at the preceding step l−1.

1. Calculation of SINR^(l)

It is shown that:

${SINR}^{l} = {\left\lbrack {\frac{1}{\xi^{l} \cdot {\mathbb{e}}^{\xi^{l}} \cdot {E_{1}\left( \xi^{l} \right)}} - 1} \right\rbrack \cdot \frac{1}{\left( {1 - \left( \rho^{l - 1} \right)^{2}} \right)}}$with

${\frac{1}{\xi^{l}} = \frac{1 - \left( \rho_{s}^{l - 1} \right)^{2}}{\zeta}};{\frac{1}{\zeta} = {\frac{N \cdot E_{s}}{N_{0}} = \frac{N}{M \cdot N_{0}}}}$${{{and}\mspace{14mu}{E_{1}(s)}} = {\int_{s}^{+ \infty}{\frac{e^{- t}}{t}\ {\mathbb{d}t}}}},$the integral exponential.

2. Calculation of ρ^(l)

The calculation of ρ^(l) is done in several steps:

-   a—Let ρ⁰=0 and l=1-   b—Calculate the signal to interference (+noise) ratio at the    threshold detector input using the formula:

${SINR}^{l} = {\left\lbrack {\frac{1}{\xi^{l} \cdot {\mathbb{e}}^{\xi^{l}} \cdot {E_{1}\left( \xi^{l} \right)}} - 1} \right\rbrack \cdot \frac{1}{\left( {1 - \left( \rho^{l - 1} \right)^{2}} \right)}}$

-   c—Calculate the symbol error probability Pr at the threshold    detector input from the SINR^(l) assuming that the total noise is    Gaussian and using the formula corresponding to the constellation,    for example in the case of an m-PSK type modulation, the following    formula can be used:

$\Pr = {2 \cdot {{Q\left( {{\sin\left( \frac{\pi}{m} \right)} \cdot \sqrt{2 \cdot {SINR}^{l}}} \right)}.}}$This calculation results from an approximation to a strong signal tonoise ratio for the symbol error probabilities of the m-PSK modulationsassociated with a threshold detector symbol by symbol in the presence ofan additive white Gaussian noise type channel. This approximation islinked to the definition of the equivalent model.

-   d—Calculate the expression of ρ^(l) at the subtractor output    assuming that when there is an error, then the threshold detector    detects one of the closest neighbours to the symbol transmitted. In    the case of an m-PSK, this results in:

$\rho^{l} \approx {1 - {2 \cdot {\sin^{2}\left( \frac{\pi}{m} \right)} \cdot \Pr}}$

-   e—Increment l (l=l+1) and return to step b.

As seen in FIG. 2, the architecture of the decoder according to theinvention shows soft decisions at the output of the subtractor 9. Thesedecisions are exploited at the final iteration. They can be injectedinto a soft input decoder 6.

By calling the final iteration L, it is possible to approximate {tildeover (s)}^(L) by the following equation:{tilde over (s)} ^(L) =K S+noiseWhere constant K>0 is known and S is the column vector of the symbolswith MT components.

If the soft or weighted input decoder is a Viterbi algorithm, it willonly have to minimize the euclidian distance between {tilde over(s)}^(L) and KS on all the error-correcting code words.

FIG. 3 shows a general block diagram of the decoder according to theinvention. The decoding module 11 comprises the elements B, D, 9 and 10of FIG. 2. In fact the vector Y at the input, and a soft output {tildeover (s)}^(L) (output of the subtractor 9) as well as the output ŝ^(l)(output of the threshold detector 10) are found. It shows a module 12for calculation of the coefficients of the matrices B and D. This module12 makes it possible to calculate, at each iteration or overall beforethe start of the iterations, the correlation coefficient and thecoefficients bl and dl of the matrices B and D. This module 12 receivesat the input the matrix H (estimation of the transmission channel) andthe variance N₀. It can generate at the output the correlationcoefficient which can be used to interrupt the iterations or for anyother use.

Of course the invention is not limited to the examples which have justbeen described and numerous of adjustments can be to these exampleswithout going beyond the scope of the invention.

1. An iterative method for decoding a signal vector Y obtained from Nsampled signals in a space-time communication system with M transmissionantennae and N receiving antennae, with N and M being integers and Ngreater than or equal to M, with a view to obtaining an estimation ofsymbols of signals transmitted; characterized in that each iterationcomprises the following steps: Pre-processing of the vector Y in orderto maximize a signal to noise+interference ratio in order to obtain asignal {tilde over (r)}^(l), Subtraction from the signal {tilde over(r)}^(l) of a signal {circumflex over (z)}^(l) by means of a subtractor,the signal {circumflex over (z)}^(l) being obtained by reconstructionpost-processing of an interference between symbols of an iteration inprogress from symbols estimated during a preceding iteration, Detectionof a signal generated by the subtractor in order to obtain, for theiteration in progress, an estimation of the symbols of the signalstransmitted; and in that, the N signals being processed by timeintervals T corresponding to a time length of a linear space-time codeassociated with the signals transmitted, the pre-processing steputilizes a matrix B in order to maximize the signal tonoise+interference ratio, a transfer function of which is:$B^{l} = {{{{Diag}\left( \frac{1}{{\rho_{l - 1}^{2}A_{i}^{l}} + \frac{N_{0}}{E_{s}}} \right)}\mspace{14mu} 1} \leq i \leq {{{MT} \cdot C^{H}}V^{l}}}$${{{with}\mspace{14mu} V^{l}} = \left\lbrack {{\frac{1 - \rho_{l - 1}^{2}}{\frac{N_{0}}{E_{s}}} \cdot C \cdot C^{H}} + {Id}_{N}} \right\rbrack^{- 1}};{A^{l} = {{diag}\left( {C^{H} \cdot V^{l} \cdot C} \right)}};$wherein Λ: iteration index; ρ: standardized correlation coefficientbetween real symbols and estimated symbols; N₀: noise variance; Es: meanenergy of a symbol; C: extended channel matrix; Id_(N): identity matrixof size N; C^(H): conjugate transpose of C; i: index ranging from 1 toMT; and in that a post-processing step involves a matrix D for thereconstruction of the interference between symbols, a transfer functionof which is:$D^{l} = {{{B^{l} \cdot C \cdot \rho_{l - 1}} - {{{Diag}\left( \frac{1}{{\rho_{l - 1}^{2}A_{i}^{l}} + \frac{N_{0}}{E_{s}}} \right)}1}} \leq i \leq {{MT}.}}$2. The method according to claim 1, wherein the pre-processing step iscarried out by operating a matrix multiplication between the signalvector Y and a matrix B, the matrix B being updated at each iteration.3. The method according to claim 1, wherein the post-processing step iscarried out by operating a matrix multiplication between the estimationof the symbols of the signals transmitted during the preceding iterationand the matrix D, the matrix D being updated at each iteration.
 4. Themethod according to claim 2, wherein for each iteration, thestandardized correlation coefficient ρ is calculated and the matrix B isupdated, the updating of the matrix B being achieved by determining newcoefficients of the matrix B as a function of the correlationcoefficient obtained for a preceding iteration.
 5. The method accordingto claim 1, wherein in order to determine the correlation coefficientρ^(l) for each iteration: the signal to noise+interference ratio SINRfor each iteration is calculated using the following formula:${SINR}^{l} = {\left\lbrack {\frac{1}{\xi^{l}{\mathbb{e}}^{\xi^{l}}{E_{1}\left( \xi^{l} \right)}} - 1} \right\rbrack\frac{1}{1 - \rho_{l - 1}^{2}}}$and defining the integral exponential${E_{1}(s)} = {{\int_{s}^{+ \infty}{\frac{e^{- t}}{t}\ {\mathbb{d}t}\mspace{14mu}{with}\mspace{14mu}\xi^{l}}} = {{\frac{ϛ}{1 - \rho_{l - 1}^{2}}\mspace{14mu}{and}\mspace{14mu} ϛ} = \frac{N_{0}}{{NE}_{s}}}}$with ξ^(l)=ζ/1−ρ_(l−1) ² and ζ=N₀/NE_(S) a symbol error probability Pris calculated from the signal to noise+interference ratio SlNR^(l) foreach iteration; and the correlation coefficient ρ^(l) for each iterationis then calculated from the respective symbol error probability Pr forthe given iteration.
 6. The method according to claim 5, wherein it isassumed that ρ⁰=0.
 7. The method according to claim 5, wherein in orderto calculate the symbol error probability Pr it is assumed that thetotal noise is Gaussian.
 8. The method according to claim 7, wherein, inobtaining an estimation of the symbols of the signals transmitted, aformula corresponding to a constellation originating from a linearmodulation transmission technique is used.
 9. The method according toclaim 5, wherein in order to calculate the correlation coefficient ρ^(l)for each iteration using its respective symbol error probability Pr, itis assumed that when there is an error, a threshold detector detects oneof among closest neighbors to a symbol transmitted.
 10. The methodaccording to claim 1, wherein at a final iteration, a signal leaving thesubtractor is introduced into a soft-input decoder.
 11. The methodaccording to claim 1, wherein information symbols of the N sampledsignals are elements of a constellation originating from quadratureamplitude modulation.
 12. A space-time decoder for decoding a signalvector Y obtained from N sampled signals in a space-time communicationsystem with M transmission antennae and N receiving antennae, with N andM being integers and N greater than or equal to M, with a view toobtaining an estimation of symbols of signals transmitted, characterizedin that it comprises: a pre-processing module of the vector Y formaximizing a signal to noise+interference ratio in order to obtain asignal {tilde over (r)}^(l), a post-processing module for reconstructionof an interference between symbols from symbols estimated during apreceding iteration in order to generate the signal {circumflex over(z)}^(l), a subtractor for subtracting a signal {circumflex over(z)}^(l) from the signal {tilde over (r)}^(l), a threshold detector fordetecting a signal generated by the subtractor in order to obtain, foran iteration in progress, an estimation of the symbols of the signalstransmitted; and in that the N sampled signals being processed byintervals of time T corresponding to a time length of a linearspace-time code associated with the signals transmitted, thepre-processing module utilizes a matrix B for maximizing the signal tonoise+interference ratio, a transfer function of which is:$B^{l} = {{{{Diag}\left( \frac{1}{{\rho_{l - 1}^{2}A_{i}^{l}} + \frac{N_{0}}{E_{s}}} \right)}1} \leq i \leq {{{MT} \cdot C^{H}}V^{l}}}$${{{with}\mspace{14mu} V^{l}} = \left\lbrack {{\frac{1 - \rho_{l - 1}^{2}}{\frac{N_{0}}{E_{S}}} \cdot C \cdot C^{H}} + {Id}_{N}} \right\rbrack^{- 1}};{A^{l} = {{diag}\left( {C^{H} \cdot V^{l} \cdot C} \right)}};$wherein l: iteration index; ρ: standardized correlation coefficientbetween the real symbols and the estimated symbols; N₀: noise variance;Es: mean energy of a symbol; C: extended channel matrix; Id_(N):identity matrix of size N; C^(H): conjugate transpose of C; i: indexranging from 1 to MT; and in that the post-processing module consists ofa matrix D for the reconstruction of the interference between symbols, atransfer function of which is:$D^{l} = {{{B^{l} \cdot C \cdot \rho_{l - 1}} - {{{Diag}\left( \frac{1}{{\rho_{l - 1}^{2}A_{i}^{l}} + \frac{N_{0}}{E_{S}}} \right)}1}} \leq i \leq {{MT}.}}$13. The decoder according to claim 12, wherein it further comprises asoft input decoder receiving the signal generated from the subtractorduring a final iteration.